[Pw_forum] Allowed symmetries in GIPAW

Davide Ceresoli davide.ceresoli at cnr.it
Mon Jul 10 11:01:09 CEST 2017

```Dear Nelson,
95% I think that fractional translation are allowed, because they
shift rigidly the cartesian reference frame. 5% I will be proven
wrong by experts in group theory and symmetry.

Best wishes,
Davide

On 07/10/2017 10:47 AM, J. Nelson wrote:
> Dear Davide,
>
> Thanks very much for your explanation.
>
> Could I check one further example with you. This one is (x,y,z) => (-x,y,-z),
> but, it has a fractional translation as well:
>
>      isym =  3     180 deg rotation - cart. axis [0,1,0]
>
> cryst. s( 3) = (     0         -1          0      )  f =( -0.5000000 )
>                (    -1          0          0      )     ( -0.5000000 )
>                (     0          0         -1      )     ( -0.5000000 )
>
> cart.  s( 3) = ( -1.0000000  0.0000000  0.0000000 )  f =( -0.3026487 )
>                (  0.0000000  1.0000000  0.0000000 )     (  0.0000000 )
>                (  0.0000000  0.0000000 -1.0000000 )     ( -0.4029274 )
>
> Would this be allowed in GIPAW?
>
> Many thanks,
>
> Joseph Nelson
> TCM Group
> Cavendish Laboratory
> University of Cambridge
>
>
> On 2017-07-08 14:41, Davide Ceresoli wrote:
>> Dear Joseph,
>>      that operation is allowed because x=>x, y=>-y, z=>-z,
>> if I read correctly. The cartesian matrices can be off
>> diagonal. For example the rotation of 90° along z, is also
>> allowed, because the triplet (x,y,z) => (-y,x,z) is still
>> parallel to the original.
>>
>> Basically the problems are with hexagonal crystals and
>> with system with very low symmetry.
>>
>> For hexagonal crystals, it's better to use ibrav=0, and
>> set a,b in the xy plane, c//z, a forming an angle of 30°
>> with x.
>>
>> In all other cases, if unsure, set nosym=.true. in the SCF
>> calc.
>>
>> Best wishes,
>>      Davide
>>
>>
>> On 07/07/2017 12:35 PM, J. Nelson wrote:
>>> Dear all QE users,
>>>
>>> I am using QE-6.1.
>>>
>>> The user guide for GIPAW explains that 'symmetry operations that do not map
>>> cartesian axes are not allowed (i.e. 120 deg. rotations)'.
>>>
>>> Does this mean that the Cartesian rotation matrices for each symmetry operation
>>> - e.g.:
>>>
>>>       isym =  4     180 deg rotation - cart. axis [1,0,0]
>>>
>>>  cryst.   s( 4) = (     0          1          0      )
>>>                   (     1          0          0      )
>>>                   (     0          0         -1      )
>>>
>>>  cart.    s( 4) = (  1.0000000  0.0000000  0.0000000 )  [<--this matrix here]
>>>                   (  0.0000000 -1.0000000  0.0000000 )
>>>                   (  0.0000000  0.0000000 -1.0000000 )
>>>
>>> need to be diagonal for the symmetry operation to be compatible with GIPAW? Are
>>> symmetry operations with an associated fractional translation allowed?
>>>
>>>
>>> Many thanks,
>>>
>>> Joseph Nelson
>>> TCM Group
>>> Cavendish Laboratory
>>> University of Cambridge
>>>
>

```